I wouldn't dig it in, any pieces that aren't decomposed will borrow nitrogen from the soil while they rot down. You could part the surface mulch and plant direct into the soil below (it should be really soft after two years of being covered) but with wood chips I found working like this the plants really needed / benefited from a sprinkling of BFB or chicken manure pellets at time of planting.
Mulching with wood chips was bought to the fore by a chap called Paul Gautschi - who named it The Back To Eden Method. What most folk miss when going down the BTE route is Paul uses chips that are about three years old and then he passes them through his large chicken run (where they mix with the droppings) before being spread on his growing beds.
If you're not intending to run the plot as no-dig it'd pay you to rake off as many of the big bits of wood as you can.
Edit to say - the raked up chippings would make good paths between your beds. Worms love it and as the paths decompose they'll add nutrients to the soil. Wood chip paths can be walked on at any time of year without damaging the soil structure below.
